Prediction intervals for time series and their applications to portfolio selection

This study considers prediction intervals for time series and applies the results to portfolio selection. The dynamics of the high and low underlying returns are depicted by time series models, which lead to a prediction interval of future returns. We propose an innovative criterion for portfolio selection based on the prediction interval. A new concept of coherent risk measures for the interval of returns is introduced. An empirical study is conducted with the stocks of the Dow Jones Industrial Average Index. A self-financing trading strategy is established by daily reallocating the holding positions via the proposed portfolio selection criterion. The numerical results indicate that the proposed prediction interval has promising coverage, efficiency and accuracy for prediction. The proposed portfolio selection criterion constructed from the prediction intervals is capable of suggesting an optimal portfolio according to the economic conditions.